RESULTS OF BIRTHDAY SPACINGS FOR dh-ranFile-2015-06-29_18:31 (no_bdays=1024, no_days/yr=2^24, lambda=16.00, sample size=500) Bits used mean chisqr p-value 1 to 24 16.00 7.4144 0.022479 2 to 25 15.53 20.8186 0.765490 3 to 26 15.55 20.1372 0.732726 4 to 27 15.72 19.6915 0.709686 5 to 28 15.67 9.4668 0.075532 6 to 29 15.73 15.1903 0.418227 7 to 30 15.92 18.5894 0.647398 8 to 31 15.89 18.3379 0.632171 9 to 32 15.36 26.5254 0.934594 Chisquare degrees of freedom: 17 --------------------------------------------------------------- p-value for KStest on those 9 p-values: 0.556647 Tough bday spacings test for dh-ranFile-2015-06-29_18:31: 4096 birthdays, year=2^32 days Table of Expected vs. Observed counts: Duplicates 0 1 2 3 4 5 6 7 8 9 >=10 Expected 9.2 36.6 73.3 97.7 97.7 78.1 52.1 29.8 14.9 6.6 4.1 Observed 12 41 73 103 96 66 50 34 11 9 5 (O-E)^2/E 0.9 0.5 0.0 0.3 0.0 1.9 0.1 0.6 1.0 0.9 0.2 Birthday Spacings: Sum(O-E)^2/E= 6.384, p= 0.218 RESULTS OF GCD FOR dh-ranFile-2015-06-29_18:31 Euclid's algorithm: p-value, steps to gcd: 0.798647 p-value, dist. of gcd's: 0.640616 Gorilla test for 2^26 bits, positions 0 to 31 for dh-ranFile-2015-06-29_18:31: Note: lengthy test---for example, ~20 minutes for 850MHz PC Bits 0 to 7---> 0.436 0.917 0.181 0.634 0.863 0.889 0.673 0.869 Bits 8 to 15---> 0.426 0.219 0.703 0.365 0.640 0.047 0.080 0.527 Bits 16 to 23---> 0.915 0.761 0.830 0.770 0.940 0.163 0.772 0.205 Bits 24 to 31---> 0.438 0.133 0.934 0.892 0.868 0.880 0.063 0.478 KS test for the above 32 p values: 0.889 The OPERM5 test for 10 million (overlapping) 5-tuples for dh-ranFile-2015-06-29_18:31, p-values for 5 runs: 0.6208, 0.1397, 0.0544, 0.2619, 0.5242 Rank test for binary matrices (31x31) for dh-ranFile-2015-06-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=28 195 211.4 1.275 1.275 r= 29 5114 5134.0 0.078 1.353 r= 30 23223 23103.0 0.623 1.976 r= 31 11468 11551.5 0.604 2.580 chi-square = 2.580 with df = 3; p-value = 0.539 -------------------------------------------------------------- Rank test for binary matrices (32x32) for dh-ranFile-2015-06-29_18:31 RANK OBSERVED EXPECTED (O-E)^2/E SUM r<=29 218 211.4 0.205 0.205 r= 30 5152 5134.0 0.063 0.268 r= 31 23052 23103.0 0.113 0.381 r= 32 11578 11551.5 0.061 0.441 chi-square = 0.441 with df = 3; p-value = 0.068 -------------------------------------------------------------- Rank test for binary matrices (6x8) for dh-ranFile-2015-06-29_18:31 b-rank test for bits 1 to 8, p=0.56689 b-rank test for bits 2 to 9, p=0.50638 b-rank test for bits 3 to 10, p=0.13765 b-rank test for bits 4 to 11, p=0.17724 b-rank test for bits 5 to 12, p=0.39488 b-rank test for bits 6 to 13, p=0.45264 b-rank test for bits 7 to 14, p=0.98946 b-rank test for bits 8 to 15, p=0.75107 b-rank test for bits 9 to 16, p=0.48594 b-rank test for bits 10 to 17, p=0.44000 b-rank test for bits 11 to 18, p=0.98090 b-rank test for bits 12 to 19, p=0.23350 b-rank test for bits 13 to 20, p=0.15530 b-rank test for bits 14 to 21, p=0.05730 b-rank test for bits 15 to 22, p=0.11730 b-rank test for bits 16 to 23, p=0.55188 b-rank test for bits 17 to 24, p=0.56898 b-rank test for bits 18 to 25, p=0.72660 b-rank test for bits 19 to 26, p=0.81146 b-rank test for bits 20 to 27, p=0.61592 b-rank test for bits 21 to 28, p=0.21896 b-rank test for bits 22 to 29, p=0.04652 b-rank test for bits 23 to 30, p=0.80040 b-rank test for bits 24 to 31, p=0.99106 b-rank test for bits 25 to 32, p=0.97813 TEST SUMMARY, 25 tests, each on 100,000 random 6x8 matrices The above should be 25 uniform [0,1] random variables: The KS test for those 25 supposed UNI's yields p = 0.504249 THE OVERLAPPING 20-TUPLES BITSTREAM TEST for dh-ranFile-2015-06-29_18:31 (20 bits/word, 2097152 words 20 bitstreams. No. missing words should average 141909.33 with sigma=428.00.) ---------------------------------------------------------------- BITSTREAM test results. Bitstream No. missing words z-score p-value 1 141886 -0.05 0.478265 2 141880 -0.07 0.472683 3 142055 0.34 0.633204 4 141753 -0.37 0.357460 5 142700 1.85 0.967653 6 141538 -0.87 0.192808 7 141514 -0.92 0.177830 8 141817 -0.22 0.414601 9 141185 -1.69 0.045289 10 141995 0.20 0.579324 11 141591 -0.74 0.228510 12 142206 0.69 0.755894 13 142304 0.92 0.821769 14 141823 -0.20 0.420073 15 141895 -0.03 0.486645 16 142171 0.61 0.729526 17 141451 -1.07 0.142115 18 142499 1.38 0.915857 19 141863 -0.11 0.456900 20 141699 -0.49 0.311563 ---------------------------------------------------------------- OPSO test for dh-ranFile-2015-06-29_18:31 Bits used No. missing words z-score p-value 23 to 32 141679 -0.7942 0.213528 22 to 31 141989 0.2747 0.608236 21 to 30 141657 -0.8701 0.192122 20 to 29 141366 -1.8736 0.030496 19 to 28 141337 -1.9736 0.024216 18 to 27 141971 0.2127 0.584202 17 to 26 142384 1.6368 0.949163 16 to 25 142181 0.9368 0.825568 15 to 24 142467 1.9230 0.972760 14 to 23 141970 0.2092 0.582857 13 to 22 142111 0.6954 0.756602 12 to 21 141690 -0.7563 0.224732 11 to 20 142217 1.0609 0.855639 10 to 19 141362 -1.8873 0.029557 9 to 18 141967 0.1989 0.578815 8 to 17 141844 -0.2253 0.410882 7 to 16 142010 0.3471 0.635756 6 to 15 141822 -0.3011 0.381655 5 to 14 141989 0.2747 0.608236 4 to 13 141402 -1.7494 0.040110 3 to 12 141599 -1.0701 0.142286 2 to 11 142168 0.8920 0.813794 1 to 10 141753 -0.5391 0.294920 ----------------------------------------------------------------- OQSO test for dh-ranFile-2015-06-29_18:31 Bits used No. missing words z-score p-value 28 to 32 141856 -0.1808 0.428270 27 to 31 141992 0.2802 0.610352 26 to 30 141987 0.2633 0.603836 25 to 29 141557 -1.1943 0.116173 24 to 28 142234 1.1006 0.864459 23 to 27 142436 1.7853 0.962895 22 to 26 141657 -0.8554 0.196177 21 to 25 141805 -0.3537 0.361797 20 to 24 142289 1.2870 0.900956 19 to 23 141750 -0.5401 0.294564 18 to 22 141772 -0.4655 0.320778 17 to 21 141836 -0.2486 0.401844 16 to 20 141784 -0.4248 0.335474 15 to 19 141687 -0.7537 0.225526 14 to 18 141590 -1.0825 0.139521 13 to 17 142208 1.0124 0.844336 12 to 16 142021 0.3785 0.647486 11 to 15 142124 0.7277 0.766600 10 to 14 141476 -1.4689 0.070928 9 to 13 142049 0.4735 0.682057 8 to 12 141754 -0.5265 0.299256 7 to 11 142190 0.9514 0.829305 6 to 10 141650 -0.8791 0.189678 5 to 9 141663 -0.8350 0.201854 4 to 8 141188 -2.4452 0.007239 3 to 7 141728 -0.6147 0.269384 2 to 6 142067 0.5345 0.703493 1 to 5 141769 -0.4757 0.317146 ----------------------------------------------------------------- DNA test for dh-ranFile-2015-06-29_18:31 Bits used No. missing words z-score p-value 31 to 32 141639 -0.7974 0.212600 30 to 31 142165 0.7542 0.774632 29 to 30 141690 -0.6470 0.258819 28 to 29 142046 0.4032 0.656583 27 to 28 141844 -0.1927 0.423592 26 to 27 142548 1.8840 0.970216 25 to 26 141913 0.0108 0.504319 24 to 25 141933 0.0698 0.527833 23 to 24 141927 0.0521 0.520785 22 to 23 142806 2.6450 0.995916 21 to 22 141629 -0.8269 0.204138 20 to 21 142253 1.0138 0.844655 19 to 20 141598 -0.9184 0.179211 18 to 19 141242 -1.9685 0.024504 17 to 18 142504 1.7542 0.960301 16 to 17 142546 1.8781 0.969815 15 to 16 142315 1.1967 0.884282 14 to 15 142036 0.3737 0.645671 13 to 14 141782 -0.3756 0.353605 12 to 13 142369 1.3560 0.912444 11 to 12 141644 -0.7827 0.216906 10 to 11 142099 0.5595 0.712089 9 to 10 142014 0.3088 0.621248 8 to 9 142288 1.1170 0.868007 7 to 8 141916 0.0197 0.507849 6 to 7 141819 -0.2665 0.394942 5 to 6 141800 -0.3225 0.373534 4 to 5 141614 -0.8712 0.191828 3 to 4 142793 2.6067 0.995429 2 to 3 141792 -0.3461 0.364632 1 to 2 141933 0.0698 0.527833 ----------------------------------------------------------------- Test result COUNT-THE-1's in bytes for dh-ranFile-2015-06-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 2560000) chisquare z-score p-value 2504.82 0.068 0.527152 Test results for specific bytes for dh-ranFile-2015-06-29_18:31 (Degrees of freedom: 5^4-5^3=2500; sample size: 256000) bits used chisquare z-score p-value 1 to 8 2600.28 1.418 0.921929 2 to 9 2525.09 0.355 0.638665 3 to 10 2574.99 1.061 0.855548 4 to 11 2388.37 -1.579 0.057210 5 to 12 2554.89 0.776 0.781182 6 to 13 2473.20 -0.379 0.352337 7 to 14 2602.41 1.448 0.926237 8 to 15 2451.24 -0.690 0.245219 9 to 16 2452.39 -0.673 0.250381 10 to 17 2490.09 -0.140 0.444271 11 to 18 2497.62 -0.034 0.486549 12 to 19 2446.46 -0.757 0.224461 13 to 20 2489.69 -0.146 0.442048 14 to 21 2481.89 -0.256 0.398943 15 to 22 2561.41 0.869 0.807450 16 to 23 2624.20 1.756 0.960489 17 to 24 2413.10 -1.229 0.109547 18 to 25 2702.44 2.863 0.997901 19 to 26 2623.79 1.751 0.959992 20 to 27 2440.04 -0.848 0.198238 21 to 28 2564.18 0.908 0.817953 22 to 29 2533.64 0.476 0.682848 23 to 30 2552.59 0.744 0.771477 24 to 31 2542.94 0.607 0.728173 25 to 32 2441.08 -0.833 0.202337 CDPARK for dh-ranFile-2015-06-29_18:31: result of 10 tests (Of 12000 tries, the average no. of successes should be 3523.0 with sigma=21.9) No. succeses z-score p-value 3498 -1.1416 0.126820 3459 -2.9224 0.001737 3525 0.0913 0.536383 3512 -0.5023 0.307734 3545 1.0046 0.842447 3548 1.1416 0.873180 3524 0.0457 0.518210 3550 1.2329 0.891189 3536 0.5936 0.723613 3523 0.0000 0.500000 Square side=100, avg. no. parked=3522.00 sample std.=26.16 p-value of the KSTEST for those 10 p-values: 0.666390 Results for the MINIMUM DISTANCE test for dh-ranFile-2015-06-29_18:31 0.7876,0.8351,0.1484,0.4336,0.9557,0.5302,0.5486,0.7838,0.0642,0.7401, The KS test for those 10 p-values: 0.585895 The 3DSPHERES test for dh-ranFile-2015-06-29_18:31 sample no r^3 equiv. uni. 1 37.269 0.711284 2 6.201 0.186727 3 38.795 0.725597 4 7.724 0.227003 5 35.577 0.694531 6 1.535 0.049893 7 126.985 0.985489 8 17.903 0.449416 9 12.028 0.330295 10 62.126 0.873924 11 28.562 0.614051 12 60.271 0.865882 13 10.669 0.299278 14 2.011 0.064826 15 76.133 0.920957 16 2.493 0.079741 17 30.666 0.640192 18 27.530 0.600549 19 1.610 0.052265 20 39.054 0.727956 -------------------------------------------------------------- p-value for KS test on those 20 p-values: 0.826105 RESULTS OF SQUEEZE TEST FOR dh-ranFile-2015-06-29_18:31 Table of standardized frequency counts (obs-exp)^2/exp for j=(1,..,6), 7,...,47,(48,...) -0.1 -0.7 0.6 -0.3 -0.2 0.5 -0.1 -0.4 -1.2 0.6 -0.5 -0.0 1.1 0.7 1.8 0.4 0.4 0.8 -0.0 -0.3 -1.3 0.3 0.9 -1.0 -1.6 -1.2 -1.6 -1.9 -0.0 -1.5 0.5 0.4 -0.8 -0.4 1.2 1.0 -0.7 -0.4 0.1 1.5 -0.6 2.0 1.8 Chi-square with 42 degrees of freedom:39.533688 z-score=-0.269097, p-value=0.420204 _____________________________________________________________ Results of the OSUM test for dh-ranFile-2015-06-29_18:31 Test no p-value 1 0.290172 2 0.865038 3 0.498811 4 0.819135 5 0.796291 6 0.055722 7 0.477601 8 0.409251 9 0.919544 10 0.791859 _____________________________________________________________ p-value for 10 kstests on 100 sums: 0.461814 Test for lengths of runs up and runs down, 100,000 each for dh-ranFile-2015-06-29_18:31: (for k>=2, the prob. of a run of length k is 2*k/(k+1)!) Length Expected UpRuns (O-E)^2/E DownRuns (O-E)^2/E 2 66666.67 66609 0.05 66665 0.00 3 25000.00 25128 0.66 25125 0.62 4 6666.67 6628 0.22 6529 2.84 5 1388.89 1365 0.41 1398 0.06 6 238.10 228 0.43 243 0.10 7 34.72 36 0.05 30 0.64 8 4.96 5 0.00 9 3.29 p=0.06418 p=0.72795 Number of rngs required: 689178, p-value: 0.815 RESULTS OF CRAPS TEST for dh-ranFile-2015-06-29_18:31 No. of wins: Observed Expected 98104 98585.9 z-score=-2.155, pvalue=0.01557 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66506 66666.7 0.387 0.387 2 37749 37654.3 0.238 0.625 3 26820 26954.7 0.673 1.299 4 19741 19313.5 9.464 10.763 5 13785 13851.4 0.318 11.082 6 10053 9943.5 1.205 12.286 7 7064 7145.0 0.919 13.205 8 5075 5139.1 0.799 14.004 9 3645 3699.9 0.814 14.818 10 2601 2666.3 1.599 16.417 11 1838 1923.3 3.786 20.202 12 1377 1388.7 0.099 20.302 13 1024 1003.7 0.410 20.712 14 728 726.1 0.005 20.716 15 559 525.8 2.092 22.808 16 383 381.2 0.009 22.817 17 292 276.5 0.864 23.681 18 214 200.8 0.864 24.545 19 142 146.0 0.109 24.654 20 102 106.2 0.167 24.821 21 302 287.1 0.772 25.593 Chisq= 25.59 for 20 degrees of freedom, p= 0.82032 SUMMARY of craptest p-value for no. of wins: 0.015575 p-value for throws/game: 0.820318 _____________________________________________________________ RESULTS OF CRAPS TEST2 for dh-ranFile-2015-06-29_18:31 No. of wins: Observed Expected 98714 98585.9 z-score= 0.573, pvalue=0.71672 Analysis of Throws-per-Game: Throws Observed Expected Chisq Sum of (O-E)^2/E 1 66624 66666.7 0.027 0.027 2 37711 37654.3 0.085 0.113 3 26744 26954.7 1.648 1.760 4 19257 19313.5 0.165 1.925 5 14023 13851.4 2.125 4.051 6 9960 9943.5 0.027 4.078 7 7295 7145.0 3.148 7.226 8 5072 5139.1 0.875 8.101 9 3759 3699.9 0.945 9.046 10 2656 2666.3 0.040 9.086 11 1874 1923.3 1.265 10.351 12 1394 1388.7 0.020 10.371 13 975 1003.7 0.822 11.193 14 705 726.1 0.615 11.808 15 513 525.8 0.313 12.122 16 407 381.2 1.753 13.875 17 264 276.5 0.569 14.443 18 212 200.8 0.621 15.064 19 160 146.0 1.346 16.410 20 105 106.2 0.014 16.424 21 290 287.1 0.029 16.453 Chisq= 16.45 for 20 degrees of freedom, p= 0.31185 SUMMARY of craptest p-value for no. of wins: 0.716719 p-value for throws/game: 0.311847 _____________________________________________________________ ***** TEST SUMMARY ***** All p-values: 0.0017,0.0072,0.0156,0.0225,0.0242,0.0245,0.0296,0.0305,0.0401,0.0453, 0.0465,0.0471,0.0499,0.0523,0.0544,0.0557,0.0572,0.0573,0.0632,0.0642, 0.0642,0.0648,0.0684,0.0709,0.0755,0.0796,0.0797,0.1095,0.1162,0.1173, 0.1268,0.1330,0.1376,0.1395,0.1397,0.1421,0.1423,0.1484,0.1553,0.1626, 0.1772,0.1778,0.1792,0.1806,0.1867,0.1897,0.1918,0.1921,0.1928,0.1962, 0.1982,0.2019,0.2023,0.2041,0.2048,0.2126,0.2135,0.2169,0.2179,0.2190, 0.2194,0.2245,0.2247,0.2255,0.2270,0.2285,0.2335,0.2452,0.2504,0.2588, 0.2619,0.2694,0.2902,0.2946,0.2949,0.2993,0.2993,0.3077,0.3116,0.3118, 0.3171,0.3208,0.3303,0.3355,0.3523,0.3536,0.3575,0.3618,0.3646,0.3651, 0.3735,0.3817,0.3949,0.3949,0.3989,0.4018,0.4093,0.4109,0.4146,0.4182, 0.4201,0.4202,0.4236,0.4257,0.4283,0.4336,0.4359,0.4376,0.4400,0.4420, 0.4443,0.4494,0.4526,0.4569,0.4618,0.4727,0.4776,0.4779,0.4783,0.4859, 0.4865,0.4866,0.4988,0.5000,0.5042,0.5043,0.5064,0.5078,0.5182,0.5208, 0.5242,0.5272,0.5274,0.5278,0.5278,0.5302,0.5364,0.5389,0.5486,0.5519, 0.5566,0.5669,0.5690,0.5788,0.5793,0.5829,0.5842,0.5859,0.6005,0.6038, 0.6082,0.6082,0.6104,0.6141,0.6159,0.6208,0.6212,0.6322,0.6332,0.6343, 0.6358,0.6387,0.6401,0.6402,0.6406,0.6457,0.6474,0.6475,0.6566,0.6664, 0.6734,0.6821,0.6828,0.6945,0.7033,0.7035,0.7097,0.7113,0.7121,0.7167, 0.7236,0.7256,0.7266,0.7279,0.7280,0.7282,0.7295,0.7327,0.7401,0.7511, 0.7559,0.7566,0.7615,0.7655,0.7666,0.7703,0.7715,0.7722,0.7746,0.7812, 0.7838,0.7876,0.7919,0.7963,0.7986,0.8004,0.8075,0.8115,0.8138,0.8151, 0.8180,0.8191,0.8203,0.8218,0.8256,0.8261,0.8293,0.8299,0.8351,0.8424, 0.8443,0.8447,0.8555,0.8556,0.8629,0.8645,0.8650,0.8659,0.8677,0.8680, 0.8685,0.8732,0.8739,0.8802,0.8843,0.8890,0.8891,0.8912,0.8924,0.9010, 0.9124,0.9154,0.9159,0.9174,0.9195,0.9210,0.9219,0.9262,0.9343,0.9346, 0.9396,0.9492,0.9557,0.9600,0.9603,0.9605,0.9629,0.9677,0.9698,0.9702, 0.9728,0.9781,0.9809,0.9855,0.9895,0.9911,0.9954,0.9959,0.9979, Overall p-value after applying KStest on 269 p-values = 0.251100 In response to requests, we have provided a list of all the p-values produced by the tests you have chosen for this run. The individual p-values are supposed to be uniform in [0,1), but they are not necessarily independent. So even though we have applied a KSTEST to the accumulated p-values, the result is not necessarily---even if your file contains truly random bits---uniform in [0,1). But it is probably pretty close, so take that last p-value with a grain of salt. In particular, there may be some values so close to 0 or 1 that the tests they came from should be applied several more times, or new, related tests should be undertaken.